Designing Band Gap of Graphene by B and N Dopant Atoms
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Designing band gap of graphene by B and N dopant atoms Pooja Rani and V.K. Jindal1 Department of Physics, Panjab University, Chandigarh-160014, India Ab-initio calculations have been performed to study the geometry and electronic structure of boron (B) and nitrogen (N) doped graphene sheet. The effect of doping has been investigated by varying the concentrations of dopants from 2 % (one atom of the dopant in 50 host atoms) to 12 % (six dopant atoms in 50 atoms host atoms) and also by considering different doping sites for the same concentration of substitutional doping. All the calculations have been performed by using VASP (Vienna Ab-initio Simulation Package) based on density functional theory. By B and N doping p-type and n-type doping is induced respectively in the graphene sheet. While the planar structure of the graphene sheet remains unaffected on doping, the electronic properties change from semimetal to semiconductor with increasing number of dopants. It has been observed that isomers formed differ significantly in the stability, bond length and band gap introduced. The band gap is maximum when dopants are placed at same sublattice points of graphene due to combined effect of symmetry breaking of sub lattices and the band gap is closed when dopants are placed at adjacent positions (alternate sublattice positions). These interesting results provide the possibility of tuning the band gap of graphene as required and its application in electronic devices such as replacements to Pt based catalysts in Polymer Electrolytic Fuel Cell (PEFC). INTRODUCTION Graphene is the name given to a single layer of graphite, made up of sp2 hybridized carbon atoms arranged in a honeycomb lattice, consisting of two interpenetrating triangular sub-lattices A and B (Fig. 1) and is a basic building block for carbon allotropes of other dimensionalities like fullerenes and carbon nanotubes. Though it was realized in 1991 that carbon nanotubes were formed by rolling a 2D graphene sheet or a single layer from 3D graphitic crystal, the isolation of graphene sheet was not done till 2004. Since its successful experimental fabrication in 2004 [1], it has attracted enormous interest both from experimentalists and theoreticians. Its unique properties like half integer quantum Hall effect, high charge carrier mobility due to linear dispersion at the so called Dirac point and ballistic transport over long distances, finite conductivity at zero carrier concentration [2], make it an excellent candidate for the next generation of electronics by overcoming silicon-based electronics limitations [3]. A pristine graphene layer is however a zero gap semiconductor (or semimetal) with a point like Fermi surface. Some reviews on the properties of graphene have appeared in the literature, e.g. by Castro Neto et al [4] and Cooper et al [5] which describe pure graphene in detail. 1 Author with whom correspondence be made, Email: [email protected], present address: Department of Theoretical Chemistry, Technical University, D-10623 Berlin, Germany. 1 Fig1. A schematic presentation of graphene sheet. Each Bravais lattice unit cell includes two nonequivalent sites, which are denoted by A and B. A blow up of Unit Cell is shown separately, a1 and a2 are the primitive vectors. Pure graphene, though extremely interesting, suffers from zero band gap fixation which makes it uninteresting from device application point of view. The development of graphene based electronics depends on our ability to open a tunable band gap. Various approaches have been developed to fabricate high-performance graphene devices by engineering their band gaps so as to improve their semiconducting properties. One of the approaches is evidently to choose N and B and substitute them to replace C atoms to form ‘carbon alloys’. The atomic masses of these dopants is closest to Carbon which would seemingly be acceptable for carbon lattices to adjust to, and at the same time altering significantly the electronic properties of the host material because of electron rich and electron deficient nature of N and B atoms. Experimental and theoretical studies on graphene doping, do show this possibility of making p-type and n-type semiconducting graphene. In fact studies by different means like doping with heteroatoms [6, 7], chemical functionalization [8] applying electric fields and depositing graphene on substrates like SiC, SiO2) [9] have shown this possibility. Band gap opening using p-type doping using Al , Boron, NO2, NH3 ,H2O, F4-TCNQ and n-type doping using N, alkali metals has been studied in the past [7,10-14]. The observation has been that the dopant atoms can modify the electronic band structure of graphene, and open up an energy gap between the valence and conduction band. Recently, an ab-initio study of the different dopant interactions in the host graphene has also been reported which provides useful information on the behavior of dopants [15]. While Lherbie et. al [10] studied the charge mobilities and conductivity of the system by doping graphene with different concentrations of B and N impurities ( upto 4%) randomly ( without studying the band gap), Wu et. al [11] studied the band gap opening in graphene by only single atom doping of B and N. Despite some work by Y. Fan et al. [16] to tune band gap by choosing bi-layers of differently doped graphene, and X. Fan et al. [17] have primarily focussed on Boron-Nitride combination as a dopant and is changing the concentration by taking a larger number of host atoms. Manna et. al [18] have shown that the patching of graphene and h-BN sheet with 2 semiconducting and/or insulating BxNy (Cz) nanodomains of various geometrical shapes and sizes (h-BN sheet) can significantly change the electronic and magnetic properties. Despite all such work, a systematic study of exact role of concentration and position of dopant atoms in modulating the band gap has still not appeared in the literature. In the present paper we have made an effort to present a systematic study of effect of substitutional doping of boron and nitrogen in the graphene sheet by slowly increasing the concentration of doping and also considering the different isomers of same doped configuration. We choose B and N atoms both for our study, individually at this moment as dopants due to their nearly similar size to that of carbon and because of their electron deficient and electron rich character respectively, and deferring for the present using combination of B and N in host of C atoms. In the following, we outline computational details for our approach of using density functional theory and describe the results for B and N doping in section 3. These results are discussed and finally concluded in Section 4. 2. COMPUTATIONAL DETAILS Graphene is known to relax in 2-D honeycomb structure (Fig. 1) and the B and N doped graphene will be assumed to have similar structure, unless violated by energy minimization considerations. To do this analysis, geometry optimizations and electronic structure calculations have been performed by using the VASP (Vienna Ab-initio Simulation Package) [19, 20] code based on density functional theory (DFT). The approach is based on an iterative solution of the Kohn-Sham equation [21] of the density function theory in a plane-wave set with the projector-augmented wave pseudopotentials. In our calculations, the Perdew-Burke-Ernzerhof (PBE) [22] exchange-correlation (XC) functional of the generalized gradient approximation (GGA) is adopted. The plane-wave cutoff energy was set to 400 eV. The optimizations of the lattice constants and the atomic coordinates are made by the minimization of the total energy. The 5 × 5 supercell (consisting of 50 atoms) have been used to simulate the isolated sheet and the sheets are separated by larger than 12 Å along the perpendicular direction to avoid interlayer interactions. The Monkhorst-Pack scheme is used for sampling the Brillouin zone. In the calculations, the structures are fully relaxed with a Gamma–centred 7 × 7 × 1 k-mesh. During all of the calculation processes, except for the band determination, the partial occupancies were treated using the tetrahedron methodology with Blöchl corrections [23]. For band calculation, partial occupancies for each wavefunction were determined using the Gaussian smearing method with a smearing of 0.01 eV. For geometry optimizations, all the internal coordinates were relaxed until the Hellmann-Feynman forces were less than 0.005 Å. 3. RESULTS AND DISCUSSION First of all a pure graphene sheet was fully optimized, including its lattice constant, which was found to be 2.45 Å slightly less than the experimental value of 2.46 Å and the resulting C-C bond length of pure graphene is 1.41 Å which in agreement with previous results [24].The lattice constants, a1 and a2, (refer to Fig. 1) are expressed in Cartesian coordinates as a1= ao/2(3, √3) a2= ao/2(3, -√3) 3 where ao is interatomic distance or C-C bond length and has been found to be close to 1.42 Å.. Then the band structure of pure graphene was calculated and presented in Fig. 2, which is also found to be in agreement with the literature [2]. Fig.2 Optimized geometry and band structure of pure graphene sheet Subsequently, pure graphene is doped with increasing concentration of boron and nitrogen atoms. The relaxed lattice constant of doped graphene increases in case of B and decreases in case of N with increase in number of doped atoms because the covalent radius of boron is larger than carbon atom and that of nitrogen is less than carbon and this is consistent with the earlier results as summarized in the Introduction. We study six B-doped as well as N-doped configurations with 2%, 4%, 6%, 8%, 10%, 12% concentration of doping.